Cone models for nearly incompressible soil

Cones can be used to model soil in a unified strength-of-materials approach. For the vertical and rocking motions involving predominantly compressional-extensional deformation, the corresponding dilatational wave velocity tends to infinity for Poisson's ratio approaching 1/2. Based on the rigorous solution for the dynamic stiffness of a rigid disk for all frequencies, whereby the partition of the power among P-, S- and Rayleigh waves is also discussed, two special features are necessary for the vertical and rocking motions for nearly incompressible soil with Poisson's ratio between 1/3 and 1/2: (1) The appropriate wave velocity is selected as twice the shear wave velocity and not as the dilatational wave velocity; (2) A trapped mass which increases linearly with Poisson's ratio is introduced. The trapped mass can be assigned to the base mat, allowing the cone model to be constructed in the same way for all Poisson's ratios. The realization of cone models for surface foundations on a homogeneous half-space and on a layer on a flexible half-space and for embedded and pile foundations is addressed.     

Why cone models can represent the elastic half-space

In lieu of the rigorous elastodynamical approach, many problems in foundation dynamics may be solved quite accurately via simple cone models of the soil. Although these cone models are amenable to very simple analysis, they have not yet been widely accepted in engineering practice. The reservations against their use are possibly due to the fact that cones are based on non-rigorous strength-of-materials assumptions, they neglect large portions of the half-space, and cannot represent Rayleigh surface waves. These potential objections are investigated step by step and proven to be unfounded. It turns out that cone models indeed incorporate and provide valuable insight into all the salient features of rigorous solutions; the aspects omitted by cones are revealed to be of minor physical importance.     

Effects of the dynamic cross-interaction in the seismic analysis of multiple embedded foundations

A boundary element formulation of the substructure deletion method is presented for the seismic analysis of the dynamic cross-interaction between multiple embedded foundations. This approach is particularly suitable for three-dimensional foundations of any arbitrary geometrical shape and spatial location, since it requires only the discretization of the foundations’ surfaces. The surrounding soil is represented by a homogeneous viscoelastic half-space while the foundations are assumed to be rigid and subjected to incoming SH-, P-, and SV-waves arbitrarily inclined in both the horizontal and vertical planes. The proposed methodology is tested for the case of two identical embedded square foundations for different values of the foundations’ embedment and distance. The effects of the cross-interaction are outlined in the components of the impedance matrix and of the foundation input motion. © 1997 John Wiley & Sons, Ltd.     

Dynamics of rigid strip foundations embedded in orthotropic elastic soils

This study is concerned with the dynamic response of an arbitrary shaped rigid strip foundation embedded in an orthotropic elastic soil. The foundation is subjected to time-harmonic vertical, horizontal and moment loadings. The boundary-value problem related to an embedded foundation is analysed by using the indirect boundary integral equation method. The kernel functions of the integral equations are displacement and traction Green's functions of an anisotropic elastic half plane. Exact analytical solutions are used for the Green's functions. The boundary integral equation is solved by using numerical techniques. Selected numerical results are presented for the impedances of rectangular and semi-circular rigid strip foundations embedded in four types of anisotropic soils. A discussion on the influence of soil anisotropy and frequency of excitation on the impedances is presented. The versatility of the analysis is demonstrated by considering the through soil interaction between two semi-circular strip foundations.     

Filtering action of embedded massive foundations: New analytical expressions and evidence from 2 instrumented buildings

This paper deals with the effect of the foundation mass on the filtering action exerted by embedded foundations. The system under examination comprises a rigid rectangular foundation embedded in a homogeneous isotropic viscoelastic half‐space under harmonic shear waves propagating vertically. The problem is addressed both theoretically and numerically by means of a hybrid approach, where the foundation mass is explicitly included in the kinematic interaction between the foundation and the surrounding soil, thus referring to a “quasi‐kinematic” interaction problem. Based on the results of an extensive parametric study, it is shown that the filtering problem depends essentially on three dimensionless parameters, i.e.: the dimensionless frequency of the input motion, the foundation width‐to‐embedment depth ratio, and the foundation‐to‐soil mass density ratio. In complements to the translational and rotational kinematic interaction factors that are commonly adopted to quantify the filtering effect of rigid massless foundations on the free‐field motion, an additional kinematic interaction factor is introduced, referring to the horizontal motion at the top of a rigid massive foundation. New analytical expressions for the above kinematic interaction factors are proposed and compared with foundation‐to‐free‐field transfer functions computed from available earthquake recordings on two instrumented buildings in LA (California) and Thessaloniki (Greece). Results indicate that the foundation mass can have a strong beneficial effect on the filtering action with increasing foundation‐to‐soil mass density and foundation width‐to‐embedment depth ratios.     

Displacement solutions for dynamic loads in transversely-isotropic stratified media

Solutions for the displacements caused by dynamic loads in a viscoelastic transversely-isotropic medium are derived. The medium extends horizontally to infinity, but is bounded below by a rigid base. Stratification of the medium presents no difficulties. The medium is discretized in the vertical direction only; discretization in the horizontal direction is obviated by use of analytical solutions to the equations of motion. Application of the displacement solutions to soil-structure interaction is illustrated. A soil flexibility matrix (and hence, a stiffness matrix) for a surface foundation follows directly from the displacement solutions. A simple modification to obtain the soil stiffness for an embedded foundation of arbitrary geometry is described. Stiffnesses of rigid surface and embedded foundations are computed and compared with previously published results. In addition, the dynamic stiffness of a rigid surface foundation on a soil layer with linearly increasing shear modulus is compared to that for a homogeneous soil layer. A reduction in radiation damping is found to result from the inhomogeneity.     

A SIMPLIFIED METHOD FOR PREDICTION OF KINEMATIC SOIL–FOUNDATION INTERACTION EFFECTS ON PEAK HORIZONTAL ACCELERATION OF A RIGID FOUNDATION

The kinematic soil–foundation interaction changes the free field ground motion to a different motion at the foundation of a structure. This interaction effect may be expressed by the ratio of the peak horizontal acceleration of a rigid and relatively lightweight foundation to the peak horizontal acceleration at the ground surface in the free field. It is found that the interaction effect can be defined by a simple function of the ratio of the peak horizontal ground velocity and ground acceleration in the free field, the length of the foundation and the shear wave velocity in the soil. Predictive equations for the kinematic soil foundation effect are derived using 350 strong motion records generated by 114 earthquakes world-wide. At the same time, an attenuation relationship is derived for the ratio of the peak horizontal ground velocity and acceleration from the same set of data. Ten case histories are studied; the interaction effects are calculated by using the predictive equations and then compared with measured field values. The results of the comparison illustrate the degree of predictive capability of the method when the foundation mass and the inertial soil–foundation interaction are not considered.     

Antiplane response of a dike on flexible embedded foundation to incident SH-waves

The response of an elastic circular wedge on a flexible foundation embedded into a half-space is investigated in the frequency domain for incident pane SH-waves. The problem is solved by expansion of the motion in all three media (wedge, foundation and half-space) in cylindrical wave functions (Fourier-Bessel series). The structural model is simple, but accounts for both differential motions of the base and for the effects of soil-structure interaction. Usually, structural models in earthquake engineering consider either differential ground motion, but ignore soil-structure interaction, or consider soil-structure interaction, but for a rigid foundation, thus ignoring differential ground motion. The purpose of the study is to find how stiff the foundation should be relative to the soil so that the rigid foundation assumption in soil-structure interaction models is valid. The shortest wavelength of the incident waves considered in this study is one equal to the width of the base of the wedge. It is concluded that, for this model, a foundation with same mass density as the soil but 50 times larger shear modulus behaves as ‘rigid’. For ratio of shear moduli less than 16, the rigid foundation assumption is not valid. Considering differential motions is important because of additional stresses in structures that are not predicted by fixed-base and rigid foundation models.     

Dynamic analysis of 3-D flexible embedded foundations by a frequency domain BEM-FEM

A study on the dynamic response of three-dimensional flexible foundations of arbitrary shape, embedded in a homogenous, isotropic and linear elastic half-space is presented. Both massive and massless foundations are considered. The soil-foundation system is subjected to externally applied forces, and/or to obliquely incident seismic waves. The numerical method employed is a combination of the frequency domain Boundary Element Method, which is used to simulate the elastic soil medium, and the Finite Element Method, on the basis of which the stiffness matrix of the foundation is obtained. The foundation and soil media are combined by enforcing compatibility and equilibrium conditions at their common interface. Both relaxed and completely bonded boundary conditions are considered. The accuracy of the proposed methodology is partially verified through comparison studies with results reported in the literature for rigid embedded foundations.     

回填土场地强震动性质讨论

本文旨在讨论位于回填土场地上及回填土场地深挖基坑内的强震动观测仪所获得地震动是否是真实自由场地震动,若不是,其影响如何?结合回填土场地的强震动观测台站建设的实际情形,建立了回填土场地和回填土场地深挖基坑的有限元分析模型,基于集中质量显式动力有限元数值模拟方法,分析了回填土的波速和厚度、基坑尺寸对自由场地震动的影响.同时,提出了通过用重塑土置换回填土以降低回填土对自由场地震动影响的措施,并对重塑土置换回填土的效果进行了数值模拟分析.结果表明:回填土上和回填土深挖基坑内的地震动峰值和反应谱值与原始场地的均有明显的差异,随着回填土厚度和基坑深度的增加,其差异越大;通过重塑土置换回填土可以减小回填土对场地地震动的影响.本文所得关于回填土、基坑和重塑土的影响规律可为回填土场地上强震动观测结果的合理利用以及强震动观测台站建设提供依据.     

Torsional response of a rigid circular foundation on a saturated half-space to SH waves

An analytical approach is used to study the torsional vibrations of a rigid circular foundation resting on saturated soil to obliquely incident SH waves. Biot’s poroelastic dynamic theory is considered to characterize the saturated soil below the foundation, which is solved by Hankel transform later. In order to consider the scattering phenomena caused by the existence of the foundation, the total wave field in soil is classified into free-field, rigid-body scattering field and radiation scattering field. According to the classification of wave field and the mixed boundary-value conditions between the soil and the foundation, torsional vibrations of the foundation are formulated in two sets of dual integral equations. Then, the dual integral equations are reduced to Fredholm integral equation of the second kind to be solved. Combining with the dynamic equilibrium equations of the foundation, the expressions for the torsional vibrations of the foundation are obtained. Numerical results are presented to demonstrate the influence of excitation frequency, incident angle, the torsional inertia moment of the foundation and permeability of the saturated half-space on the torsional vibrations of the foundation.     

液化场地桩-土地震相互作用p-y曲线分析方法研究

目前,我国尚缺乏液化场地桩-土-桥梁结构地震相互作用分析的合理数值模型与简化分析方法。鉴于此,直接针对振动台试验,基于非线性文克尔地基梁模型,考虑桩周参振土的质量惯性力、上部结构的惯性力、土体辐射阻尼等效应,建立了液化场地桩-土-桥梁结构地震相互作用的p-y曲线分析模型,并给出相应的简化方法。针对振动台试验进行了0.1g El Centro波输入下的分析,验证了桩-土地震相互作用分析方法的正确性,并且推荐了计算参数的合理选取方法,可用于液化场地桩-土地震相互作用的分析。提出的液化场地桩-土地震相互作用p-y曲线简化分析方法,为实际桥梁桩基抗震设计与分析提供一定参考。     

风荷载作用下的土-结构动力特性分析

结构的动力特性直接影响到动力荷载的作用效应。动力特性分析中,土体的影响不可忽视。与地震荷载不同,动风荷载自结构向土体传播,土体的惯性力可以忽略。无质量地基法可以满足针对风荷载的土-结构动力分析的要求。本文首先推导土-结构动力相互作用的运动方程,在此基础上,以剪力墙箱型基础结构为基本分析对象,确定有限地基域的范围,分析土-结构整体动力特性。认为：足够的基础埋深,可以有效控制建筑物的摆动;为控制建筑物的动力特性,可以采取措施适当使地基土增加一定的刚度;如何在上部结构的质量和刚度之间建立对应关系以控制土-结构系统的动力特性,有待进一步研究。     

Soil-structure interaction on shallow rigid circular foundation: plane SH waves from far-field earthquakes

A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is presented. This research generalizes the previous solution by Trifunac in 1972, which tackled only the semi-circular foundation, to arbitrary shallow circular-arc foundation cases, and is thus comparatively more realistic. Ground surface displacement spectra at higher frequencies are also obtained. As an analytical series solution, the accuracy and error analysis of the numerical results are also discussed. It was observed from the results that the rise-to-span ratio of the foundation profi le, frequency of incident waves, and mass ratios of different media(foundation-structure-soil) are the three primary factors that may affect the surface ground motion amplitudes near the structure.     

Wavelet‐based non‐stationary seismic rocking response of flexibly supported tanks

The non‐stationary rocking response of liquid storage tanks under seismic base excitations including soil interaction has been developed based on the wavelet domain random vibration theory. The ground motion has been characterized through statistical functionals of wavelet coefficients of the ground acceleration history. The tank–liquid–foundation system is modelled as a multi‐degree‐of‐freedom (MDOF) system with both lateral and rocking motions of vibration of the foundation. The impulsive and convective modes of vibration of the liquid in the tank have been considered. The wavelet domain coupled dynamic equations are formulated and then solved to get the expressions of instantaneous power spectral density function (PSDF) in terms of functionals of input wavelet coefficients. The moments of the instantaneous PSDF are used to obtain the stochastic responses of the tank in the form of coefficients of hydrodynamic pressure, base shear and overturning base moment for the largest expected peak responses. Parametric variations are carried out to study the effects of various governing parameters like height of liquid in the tank, height–radius ratio of the tank, ratio of total liquid mass to mass of foundation, and shear wave velocity in the soil medium, on the responses of the tank. Copyright © 2003 John Wiley & Sons, Ltd.     

Effect of a forced harmonic vibration pile to its adjacent pile in layered elastic soil with double-shear model

A new model named double-shear model based on Pasternak foundation and Timoshenko beam theory is developed to evaluate the effect of a forced harmonic vibration pile to its adjacent pile in multilayered soil medium. The double-shear model takes into account the shear deformation and the rotational inertia of piles as well as the shear deformation of soil. The piles are simulated as Timoshenko beams, which are embedded in a layered Pasternak foundation. The differential equation of transverse vibration for a pile is solved by the initial parameter method. The dynamic interaction factors for the layered soil medium are obtained by the transfer matrix method. The formulation and the implementation have been verified by means of several examples. The individual shear effects of soil and piles on the interaction factors are evaluated through a parametric study. Compared to Winkler model with Euler beam, the present model gives much better results for the dynamic interaction of piles embedded in stiff soil with small slenderness ratios. Finally, the effect of a forced long pile to a short pile embedded in multilayered soil medium is studied in detail.     

Intensity measures for the seismic response of pile foundations

In this study the efficacy of various ground motion intensity measures for the seismic response of pile foundations embedded in liquefiable and non-liquefiable soils is investigated. A soil-pile-structure model consisting of a two-layer soil deposit with a single pile and a single degree-of-freedom superstructure is used in a parametric study to determine the salient features of the seismic response of the soil-pile-structure system. A suite of ground motion records scaled to various levels of intensity are used to investigate the full range of pile behaviour, from elastic response to failure. Various intensity measures are used to inspect their efficiency in predicting the seismic demand on the pile foundation for a given level of ground motion intensity. It is found that velocity-based intensity measures are the most efficient in predicting the pile response, which is measured in terms of maximum curvature or pile-head displacement. In particular, velocity spectrum intensity (VSI), which represents the integral of the pseudo-velocity spectrum over a wide period range, is found to be the most efficient intensity measure in predicting the seismic demands on the pile foundation. VSI is also found to be a sufficient intensity measure with respect to earthquake magnitude, source-to-site distance, and epsilon, and has a good predictability, thus making it a prime candidate for use in seismic response analysis of pile foundations.     

Rotational cone models for a soil layer on flexible rock half-space

The unfolded cone model used for calculating the dynamic response of a disk on the surface of a soil layer resting on flexible rock for translational motion is extended to rotational motion. The method is analogous to that for a layer on rigid rock, the only modification being that the reflection coefficient – α replaces the coefficient of total reflection – 1. The modified value of – α, which, in general, is frequency-dependent, is determined by considering one-dimensional wave propagation along the cone for the first impingement at the layer–rock interface. The low- and high-frequency limits of – α for the rotational motion are the same as for translational motion. As these limits do not depend on frequency, the dynamic analysis using cones can be performed in the familiar time domain. The transfer function constructed by addressing the reflections–refractions at the soil–rock interface and the reflections at the free surface in the unfolded cone model is highly accurate, resulting in the same accuracy of the dynamic response of a disk on a layer resting on flexible rock as that on a homogeneous half-space modelled with a cone.     

Rocking vibrations of a rigid embedded foundation in a poroelastic soil layer

An approximate analytical method is presented for the dynamic response of a rigid cylindrical foundation embedded in a poroelastic soil layer under the excitation of a time-harmonic rocking moment. The soil underlying the foundation base is represented by a single-layered poroelastic soil based on rigid bedrock while the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The accuracy of the present solution is verified by comparisons with existing solutions obtained from other researchers. Numerical results for the rocking dynamic impedance and dynamic response factor are presented to demonstrate the influence of nondimensional frequency of excitation, poroelastic soil layer thickness, depth ratio of the foundation and internal friction of the poroelastic soil.     

Experimental investigation on seismic behavior of scoured bridge pier with pile foundation

This study investigated the seismic performance and soil‐structure interaction of a scoured bridge models with pile foundation by shaking table tests using a biaxial laminar shear box. The bridge pier model with pile foundation comprised a lumped mass representing the superstructure, a steel pier, and a footing supported by a single aluminum pile within dry silica sand. End of the pile was fixed at the bottom of the shear box to simulate the scenario that the pile was embedded in a firm stratum of rock. The bridge pier model was subjected to one‐directional shakes, including white noise and earthquake records. The performance of the bridge pier model with pile foundation was discussed for different scoured conditions. It is found that the moment demand of pile increases with the increase of scoured depth whereas the moment demand of the bridge pier decreases, and this transition may induce the bridge failure mechanism transform from pier to pile. The seismic demand on scoured pile foundations may be underestimated and misinterpreted to a certain degree. When evaluating the system damping ratio with SSI, the system response may not be significantly changed even if the soil viscous damping contribution is varied. Copyright © 2014 John Wiley & Sons, Ltd.